820 resultados para History of number theory
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Mode of access: Internet.
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Vita.
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The present thesis is an analysis of Adrien-Marie Legendre s works on Number Theory, with a certain emphasis on his 1830 edition of Theory of Numbers. The role played by these works in their historical context and their influence on the development of Number Theory was investigated. A biographic study of Legendre (1752-1833) was undertaken, in which both his personal relations and his scientific productions were related to certain historical elements of the development of both his homeland, France, and the sciences in general, during the 18th and 19th centuries This study revealed notable characteristics of his personality, as well as his attitudes toward his mathematical contemporaries, especially with regard to his seemingly incessant quarrels with Gauss about the priority of various of their scientific discoveries. This is followed by a systematic study of Lagrange s work on Number Theory, including a comparative reading of certain topics, especially that of his renowned law of quadratic reciprocity, with texts of some of his contemporaries. In this way, the dynamics of the evolution of his thought in relation to his semantics, the organization of his demonstrations and his number theoretical discoveries was delimited. Finally, the impact of Legendre s work on Number Theory on the French mathematical community of the time was investigated. This investigation revealed that he not only made substantial contributions to this branch of Mathematics, but also inspired other mathematicians to advance this science even further. This indeed is a fitting legacy for his Theory of Numbers, the first modern text on Higher Arithmetic, on which he labored half his life, producing various editions. Nevertheless, Legendre also received many posthumous honors, including having his name perpetuated on the Trocadéro face of the Eiffel Tower, which contains a list of 72 eminent scientists, and having a street and an alley in Paris named after him
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The present dissertation analyses Leonhard Euler´s early mathematical work as Diophantine Equations, De solutione problematum diophanteorum per números íntegros (On the solution of Diophantine problems in integers). It was published in 1738, although it had been presented to the St Petersburg Academy of Science five years earlier. Euler solves the problem of making the general second degree expression a perfect square, i.e., he seeks the whole number solutions to the equation ax2+bx+c = y2. For this purpose, he shows how to generate new solutions from those already obtained. Accordingly, he makes a succession of substitutions equating terms and eliminating variables until the problem reduces to finding the solution of the Pell Equation. Euler erroneously assigns this type of equation to Pell. He also makes a number of restrictions to the equation ax2+bx+c = y and works on several subthemes, from incomplete equations to polygonal numbers
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The inclusion of the history of science in science curricula-and specially, in the curricula of science teachers-is a trend that has been followed in several countries. The reasons advanced for the study of the history of science are manifold. This paper presents a case study in the history of chemistry, on the early developments of John Dalton`s atomic theory. Based on the case study, several questions that are worth discussing in educational contexts are pointed out. It is argued that the kind of history of science that was made in the first decades of the twentieth century (encyclopaedic, continuist, essentially anachronistic) is not appropriate for the development of the competences that are expected from the students of sciences in the present. Science teaching for current days will benefit from the approach that may be termed the ""new historiography of science"".
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Esta tese contém dois capítulos, cada um lidando com a teoria e a história dos bancos e arranjos financeiros. No capítulo 1, busca-se extender uma economia Diamond-Dybvig com monitoramento imperfeito dos saques antecipados e realizar uma comparação do bem estar social em cada uma das alocações possíveis, como proposto em Presscott and Weinberg(2003). Esse monitoramento imperfeito é implementado a partir da comunicação indireta ( através de um meio de pagamento) entre os agentes e a máquina de depósitos e saques que é um agregado do setor produtivo e financeiro. A extensão consiste em estudar alocações onde uma fração dos agentes pode explorar o monitoramento imperfeito e fraudar a alocação contratada ao consumirem mais cedo além do limite, usando múltiplos meios de pagamento. Com a punição limitada no período de consumo tardio, essa nova alocação pode ser chamada de uma alocação separadora em contraste com as alocações agregadoras onde o agente com habilidade de fraudar é bloqueado por um meio de pagamento imune a fraude, mas custoso, ou por receber consumo futuro suficiente para tornar a fraude desinteressante. A comparação de bem estar na gama de parâmetros escolhida mostra que as alocações separadoras são ótimas para as economias com menor dotação e as agregadoras para as de nível intermediário e as ricas. O capítulo termina com um possível contexto histórico para o modelo, o qual se conecta com a narrativa histórica encontrada no capítulo 2. No capítulo 2 são exploradas as propriedade quantitativas de um sistema de previsão antecedente para crises financeiras, com as váriaveis sendo escolhidas a partir de um arcabouço de ``boom and bust'' descrito mais detalhadamente no apêndice 1. As principais variáveis são: o crescimento real nos preços de imóveis e ações, o diferencial entre os juros dos títulos governamentais de 10 anos e a taxa de 3 meses no mercado inter-bancário e o crescimento nos ativos totais do setor bancário. Essas variáveis produzem uma taxa mais elevada de sinais corretos para as crises bancárias recentes (1984-2008) do que os sistemas de indicadores antecedentes comparáveis. Levar em conta um risco de base crescente ( devido à tendência de acumulação de distorções no sistema de preços relativos em expansões anteriores) também provê informação e eleva o número de sinais corretos em países que não passaram por uma expansão creditícia e nos preços de ativos tão vigorosa.
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Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
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Intra-and inter-population genetic variability and the demographic history of Heliothis virescens (F.) populations were evaluated by using mtDNA markers (coxI, coxII and nad6) with samples from the major cotton-and soybean-producing regions in Brazil in the growing seasons 2007/08, 2008/09 and 2009/10. AMOVA indicated low and non-significant genetic structure, regardless of geographical scale, growing season or crop, with most of genetic variation occurring within populations. Clustering analyzes also indicated low genetic differentiation. The haplotype network obtained with combined datasets resulted in 35 haplotypes, with 28 exclusive occurrences, four of them sampled only from soybean fields. The minimum spanning network showed star-shaped structures typical of populations that underwent a recent demographic expansion. The recent expansion was supported by other demographic analyzes, such as the Bayesian skyline plot, the unimodal distribution of paired differences among mitochondrial sequences, and negative and significant values of neutrality tests for the Tajima's D and Fu's F-S parameters. In addition, high values of haplotype diversity ((H) over cap) and low values of nucleotide diversity (pi), combined with a high number of low frequency haplotypes and values of theta(pi)<theta(W), suggested a recent demographic expansion of H. virescens populations in Brazil. This demographic event could be responsible for the low genetic structure currently found; however, haplotypes present uniquely at the same geographic regions and from one specific host plant suggest an initial differentiation among H. virescens populations within Brazil.
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The Illinois Institute of Technology (iit) campus, Chicago, by architect Ludwig Mies van der Rohe, is often considered as a transitional work, usually acknowledged as significant for the reorientation of his professional career after he emigrated to the United States. Moreover, its favorable recognition today is somehow indicative of its relevance as a model for urban intervention in the contemporary American city and for contemporary city planning in general, not to mention the profound impact that it had on the cityscape of Chicago. However, today we know it was rather the result of a close collaboration between he and Ludwig Hilberseimer —later on, to be completed with Alfred Caldwell— who merged their personal ideas and expertise in the design for the first time. In addition to this, when one tries to locate the design within its own historical context and evaluate the sources of its approach to it, some contradictions arise. The major impact of the images produced by Mies to promote its realization —widely disseminated in most contemporary architectural periodicals— probably outshined the particular circumstances in which the design was conceived. In fact, it would never be materialized as originally presented, but it was, instead, continuously reworked according to land availability in the site —a circumstance often ignored by subsequent architectural critic, that enthusiastically praised the design even before it was fully completed. One of the main consequences of looking at iit from such a standpoint is that, when historically contextualized, one can appreciate that, due to the urban scale of its implementation process, the design had to face a complex reality very different to that initially planned by the architect, often far from his actual possibilities of intervention. Such approach is in contradiction with the common description of the design as a ‘tabula rasa’ that allegedly would have been formulated on the basis of a full denial of its context. On the contrary, the ever-changing circumstances of the design motivated a necessary re-interpretation of the relation between its executed fragments, in order to keep the original identity of the whole in an ever-changing context. This situation implied a continuous transformation of the design by means of a steady re-composition of its elements: as the number of completed buildings increased in its successive stages, their relation to their site-specific context changed, in a very particular process that these lines try to delineate. Requiring decades to be erected, neither of its authors would ever see the design finished as planned, partially because of the difficulties in acquiring the extension of land that it required. Considering the study of this process as able to provide a valuable gateway to understand the urban discourse that the architects entailed, the aim of these lines is to analyze the problems that the iit campus design had to face. As a starting point, a relationship between practice and theory in the activity of the authors implied in iit campus design has been assumed. Far from being interrupted during World War ii, strong historical evidence can be found to infer that both were developed in parallel. Consequently, the historical sequence of the preserved testimonies has been put into context, as well as their transformation while Mies remained in charge for the campus Master Plan. Notably, when seen from this perspective, some ideas already expressed during his previous European practice were still present during the design process. Particularly, Mies's particular understanding of certain architectural concepts — such as those of ‘order’ and ‘structure’—can be traced paralleling the theories about urban planning from his collaborators, a fact that possibly facilitated the campus successful development. The study of the way these ideas were actually redeveloped and modified in the American urban context, added to the specific process of the implementation of iit campus design, sheds a new light for a critical interpretation of the reasons that made it possible, and of the actual responsibility of Mies's collaborators in its overall development and final completion. RESUMEN El campus del Illinois Institute of Technology (iit) de Chicago, obra del arquitecto Ludwig Mies van der Rohe, es a menudo considerado como una obra de transición que, por lo general, ha venido siendo reconocida como relevante para la reorientación de su carrera profesional posterior a su exilio en los Estados Unidos. El reconocimiento del que goza el proyecto es indicativo, de algún modo, de su importancia como modelo para la intervención urbana en la ciudad norteamericana contemporánea y el planeamiento de la ciudad contemporánea en general, sin olvidar el profundo impacto que ha tenido sobre el paisaje urbano de Chicago. Sin embargo, hoy sabemos que el resultado se benefició de su estrecha colaboración con Ludwig Hilberseimer y se completaría más tarde con la de Alfred Caldwell, quienes unieron sus ideas y experiencia profesional en el proyecto por primera vez. Asimismo, cuando se intenta ubicar el proyecto dentro de su propio contexto histórico y evaluar los criterios de su manera de abordarlo, surgen algunas contradicciones. El considerable impacto de las imágenes producidas por Mies para impulsar su ejecución —ampliamente difundidas en la mayoría de publicaciones de arquitectura de la época— probablemente eclipsó las particulares circunstancias en las que el proyecto fue concebido. De hecho, nunca llegó a materializarse tal y como fue inicialmente presentado. Por contra, fue reelaborado de manera continua, de acuerdo a la disponibilidad de suelo en el emplazamiento; una circunstancia a menudo ignorada por la crítica posterior, que elogió con entusiasmo el proyecto antes siquiera de que fuese terminado. Una de las principales consecuencias de contemplar el iit desde semejante punto de vista es que, una vez contextualizada históricamente su puesta en obra, se puede apreciar que el arquitecto tuvo que enfrentarse a una compleja realidad urbana muy diferente a la inicialmente prevista —probablemente debido a la escala del proyecto— a menudo lejos de sus posibilidades reales de intervención. Este enfoque contradice la descripción habitual del proyecto como una ‘tabula rasa’, que supuestamente se habría formulado sobre la base de una negación completa de su contexto. Por el contrario, las circunstancias cambiantes del proyecto obligaron una necesaria reinterpretación de la relación entre sus frag mentos ejecutados, con el fin de mantener la identidad original del conjunto en un contexto en constante cambio. Esta situación implicó una continua transformación del proyecto por medio de una permanente re-composición de sus elementos: según se incrementaba el número de edificios construidos en las etapas sucesivas de desarrollo del conjunto, variaba su relación con el contexto específico en que se emplazaban, en un proceso muy particular que estas líneas tratan de perfilar. Al necesitar décadas para ser levantado, ninguno de sus autores vería el conjunto terminado según lo planificado, en parte debido a las dificultades para la adquisición de la extensión de suelo que demandaba. Asumiendo que el estudio de este proceso es capaz de proporcionar una valiosa puerta de entrada para elucidar el discurso urbano asumido por los Mies, el objetivo de estas líneas es analizar los problemas a los que el proyecto del campus del iit tuvo que enfrentarse. Como punto de partida, se ha supuesto una relación entre la práctica y la teoría en la actividad de los autores implicados en el proyecto del campus del iit. Lejos de interrumpirse durante la Segunda Guerra Mundial, existen evidencias históricas sólidas para deducir que ambas vertientes se desarrollaron en paralelo. En consecuencia, se ha contextualizado la secuencia histórica de los testimonios conservados, así como su transformación durante el periodo en que Mies estuvo a cargo del Plan General del campus. Significativamente, al ser contempladas bajo esta perspectiva, algunas ideas ya expresadas durante su práctica europea anterior resultan aún presentes durante la redacción del proyecto. En concreto, se puede trazar un paralelismo entre la comprensión particular de Mies de ciertos conceptos arquitectónicos —como los de ‘orden’ y ‘estructura’— y las teorías sobre el urbanismo de sus colaboradores, hecho que posiblemente facilitó el exitoso desarrollo del proyecto. El estudio de la manera en que estas ideas fueron reelaboradas y modificadas en el contexto urbano estadounidense, sumado al proceso específico de su aplicación en el proyecto del campus del iit, arroja una nueva luz para una interpretación crítica tanto de las razones que lo hicieron posible, como del papel real que los colaboradores de Mies tuvieron en su desarrollo y ejecución final.
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Translation of Histoire naturelle .
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Bibliography: p. 430-433.
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Mode of access: Internet.
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Mode of access: Internet.
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Mode of access: Internet.